How do I show a "model" in a movie just like it is actually in the movie?
I did not have your movie, so I substituted a brick image. I was able to achieve this result:



As you can see, it is not transparent at all, and nor is the brick background weird. I used this RenderLayer node setup:



Note the values in the Alpha Over node, which I changed to 0 and 1. The 0.527 for the Fac: value would have made your model transparent. The Premul: value could have led to the background distortions. Also note that I checked Transparent in the Properties panel > Render tab > Film dropdown. The modified Film dropdown should look like this:



Here is a modified .blend file. You will have to substitute your video back in to the RenderLayer node setup, though.